Download An Introduction to Manifolds (Universitext) by Loring W. Tu PDF

By Loring W. Tu

Manifolds, the higher-dimensional analogs of gentle curves and surfaces, are basic items in sleek arithmetic. Combining elements of algebra, topology, and research, manifolds have additionally been utilized to classical mechanics, common relativity, and quantum box theory.

In this streamlined creation to the topic, the idea of manifolds is gifted with the purpose of supporting the reader in achieving a speedy mastery of the basic subject matters. by means of the top of the ebook the reader might be capable of compute, a minimum of for easy areas, some of the most simple topological invariants of a manifold, its de Rham cohomology. alongside the way in which, the reader acquires the data and talents helpful for additional learn of geometry and topology. The considered necessary point-set topology is integrated in an appendix of twenty pages; different appendices assessment evidence from actual research and linear algebra. tricks and ideas are supplied to the various workouts and problems.

This paintings can be utilized because the textual content for a one-semester graduate or complicated undergraduate path, in addition to by way of scholars engaged in self-study. Requiring merely minimum undergraduate necessities, 'Introduction to Manifolds' can also be a very good origin for Springer's GTM eighty two, 'Differential varieties in Algebraic Topology'.

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